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Math Help - Parametric Equations of a Line

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    Parametric Equations of a Line

    I am to find the parametric and vector equations for the line passing through the given points.

    P(0, 1/2, 1) Q(2, 1, -3)
    The line through the points is parrellel to:
    V = rq - rp (q and p are subscripts correponding to points P and Q)
    V = < 2-0, 1-1/2, -3-1>
    = <2, 1/2, -4>
    R= r + Vt
    = < 0 , 1/2, 1 > + < 2t , t/2 , -4t >
    = < 2t , 1/2 + t/2 , 1-4t >
    Parametric equations
    x = 2t
    y = 1/2 + t/2
    z = 1 - 4t
    The answer in the book is:

    x = 2 + 2t
    y = 1 + t/2
    z = -3 - 4t

    I have done many questions like these and I basically do the same procedure, and I get the correct equations. I don't understand how this particular set of points is different.
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    Quote Originally Posted by adkinsjr View Post
    I am to find the parametric and vector equations for the line passing through the given points.

    P(0, 1/2, 1) Q(2, 1, -3)
    The line through the points is parrellel to:
    V = rq - rp (q and p are subscripts correponding to points P and Q)
    V = < 2-0, 1-1/2, -3-1>
    = <2, 1/2, -4>
    R= r + Vt
    = < 0 , 1/2, 1 > + < 2t , t/2 , -4t >
    = < 2t , 1/2 + t/2 , 1-4t >
    Parametric equations
    x = 2t
    y = 1/2 + t/2
    z = 1 - 4t
    The answer in the book is:

    x = 2 + 2t
    y = 1 + t/2
    z = -3 - 4t

    I have done many questions like these and I basically do the same procedure, and I get the correct equations. I don't understand how this particular set of points is different.
    The parametric equations for a line are not unique. Let t --> t - 1 in your answer and you get the book's answer.
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    Ok, thanks
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